In the asymptotic limit of long
wavelengths (\(k\ll 1\) ) and negligible confinement (\(l_x,l_y\gg 1\) ), we expect to recover the result of slender body theory [1]} given by (REF ), which writes in dimensionless form
\(f_y = - m_a (\partial _{{t}}+\partial _{{z}})^2 w,\) 
